Fiber optics apparatus and method for accurate current sensing

ABSTRACT

The fiber optics sensor includes a polarization maintaining optic fiber forming an optical loop, and a sensing medium coupled to the optic fiber and disposed generally midway in the optical loop. First and second quarter waveplates, coupled to the optic fiber and oriented at approximately 45° with one another in close proximity to the sensing medium, convert two counter-propagating linearly polarized light waves traveling in the optical loop into two counter-propagating circularly polarized light waves prior to passing through the sensing medium. The first and second quarter waveplates further convert the counter-propagating circularly polarized light waves into two linearly polarized light waves after exiting the sensing medium. The counter-propagating circularly polarized light waves passing through the sensing medium experience a differential phase shift caused by a magnetic field or current flowing in a conductor proximate to the sensing medium. A detector is coupled to the optic fiber and detects the differential phase shift and produces an output in response thereto.

RELATED PATENT APPLICATIONS

This patent application is a continuation-in-part, application of U.S.patent application titled Fiber Optics Apparatus and Method for AccurateCurrent Sensing, Ser. No. 08/691,748, and filed on Aug. 1, 1996, nowallowed U.S. Pat. No. 5,696,858.

This patent application is related to U.S. patent application titledFiber Optic Interferometric Current and Magnetic Field Sensor, U.S. Pat.No. 5,644,397, issued on Jul. 1, 1997 to James N. Blake, which is acontinuation of application Ser. No. 08/320,734, filed Oct. 7, 1994 ofthe same title and inventor, now abandoned.

TECHNICAL FIELD OF THE INVENTION

This invention relates in general to the field of fiber optic sensors.More particularly, the present invention relates to fiber opticsapparatus and method for accurate current sensing.

BACKGROUND OF THE INVENTION

Over the past decade, fiber optic sensors have received attention in theapplication of magnetic field sensing and current sensing. Fiber opticcurrent sensors are particularly advantageous over iron-core currenttransformers, since fiber optic sensors are non-conductive and lightweight. Furthermore, fiber optic sensors also do not exhibit hysteresisand provide a much larger dynamic range and frequency response.

Fiber optic current sensors work on the principle of the Faraday effect.Current flowing in a wire induces a magnetic field which, through theFaraday effect, rotates the plane of polarization of the light travelingin the optical fiber wound around the current carrying wire. Faraday'slaw, stated as:

    I=∫oH·dL

where I is the electrical current, H is the magnetic field and theintegral is taken over a closed path around the current. If the sensingfiber is wound around the current carrying wire with an integral numberof turns, and each point in the sensing fiber has a constant sensitivityto the magnetic field, then the rotation of the plane of polarization ofthe light in the fiber depends on the current being carried in the wireand is insensitive to all externally generated magnetic fields such asthose caused by currents carried in nearby wires. The angle, Δφ, throughwhich the plane of polarization of light rotates in the presence of amagnetic field is given by:

    Δφ=V∫H·dL

where V is the Verdet constant of the fiber glass. The sensing opticalfiber performs the line integral of the magnetic field along its pathwhich is proportional to the current in the wire when that path closeson itself. Thus, Δφ=VNI, where N is the number of turns of sensing fiberwound around the current carrying wire. The rotation of the state ofpolarization of the light due to the presence of an electrical currentmay be measured by injecting light with a well defined linearpolarization state into the sensing region, and then analyzing thepolarization state of the light after it exits the sensing region.

In related U.S. Pat. No. 5,644,397 entitled Fiber Optic InterferometricCurrent and Magnetic Field Sensor, issued on Jul. 1, 1997 to James N.Blake (Hereinafter "Blake"), in-line and loop fiber optic sensors formeasuring current and magnetic fields are taught. Blake is incorporatedherein by reference. Blake teaches splitting the light beam into lighttraveling on the first and second principle eigen axes, the use of abirefringence modulator to apply a waveform or waveforms to birefringentmodulate the light beam, and further the use of a quarter waveplate setat 45° to the principle axes of the fiber to convert orthogonallylinearly polarized light to counter-rotating circularly polarized lightprior to entering the sensing region. Upon reflection at the end of thefiber, the sense of rotation of the two light waves are reversed and thelight waves travel back through the sensing region, are converted backto linearly polarized light, and are propagated back to a photodetector.The two light waves therefore undergo reciprocal paths and the samepolarization evolution through the optical circuit. Blake isincorporated herein by reference.

The fiber optic sensors taught by Blake overcame many disadvantagesassociated with conventional all fiber sensors. However, the sensor andsensing method still suffers from a particularly exacerbating problemwhich affects the accuracy of the sensor. To have a very accuratemeasurement, the optical components, particularly the quarter waveplate,must be perfect and not be affected by external stresses such astemperature variations and mechanical disturbances. It is wellrecognized that perfect or nearly perfect quarter waveplates aredifficult and very costly to design and manufacture to achieve accuratesensing required by certain applications.

SUMMARY OF THE INVENTION

Accordingly, a need has arisen for apparatus and method for compensatingthe error introduced by the optical element that converts linearlypolarized light waves to circularly polarized light waves and back suchas an imperfect quarter waveplate.

In accordance with the present invention, a fiber optics sensor andmethod for accurate measurements are provided which eliminates orsubstantially reduces the disadvantages associated with prior opticalsensors.

In one aspect of the invention, a fiber optics sensor comprises apolarization maintaining optic fiber forming an optical path, and firstand second counter-propagating linearly polarized light waves travelingin the polarization maintaining optic fiber on the optical path. A firstquarter waveplate is coupled to the optic fiber and disposed in theoptical path generally adjacent to a sensing region, the first quarterwaveplate operable to convert the first linearly polarized light waveinto a circularly polarized light wave traveling on the optical pathprior to the sensing region. A second quarter waveplate is coupled tothe optic fiber and disposed in the optical path adjacent to the sensingregion, the second quarter waveplate operable to convert the secondlinearly polarized light wave into a second circularly polarized lightwave prior to the sensing region. The first and second quarterwaveplates are oriented with one another at approximately 45°. Thesecond quarter waveplate further converts the first circularly polarizedlight wave back to a first linearly polarized light wave after exitingthe sensing region, and the first quarter waveplate further converts thesecond circularly polarized light wave back to a second linearlypolarized light wave after exiting the sensing region. The sensingregion includes a sensing medium that is coupled to the polarizationmaintaining optic fiber, and the first and second circularly polarizedlight waves passing through the sensing medium experience a differentialphase shift caused by a magnetic field or current flowing in a conductorproximate to the sensing region. A detector coupled to the optic fiberdetects the differential phase shift and produces an output in responsethereto.

In another aspect of the invention, the fiber optics sensor includes apolarization maintaining optic fiber forming an optical loop, and asensing medium coupled to the optic fiber and disposed generally midwayin the optical loop. First and second quarter waveplates, coupled to theoptic fiber and oriented at approximately 45° with one another in closeproximity to the sensing medium, convert two counter-propagatinglinearly polarized light waves traveling in the optical loop into twocounter-propagating circularly polarized light waves prior to passingthrough the sensing medium. The first and second quarter waveplatesfurther convert the counter-propagating circularly polarized light wavesinto two linearly polarized light waves after exiting the sensingmedium. The counter-propagating circularly polarized light waves passingthrough the sensing medium experience a differential phase shift causedby a magnetic field or current flowing in a conductor proximate to thesensing medium. A detector coupled to the optic fiber detects thedifferential phase shift and produces an output in response thereto.

In yet another aspect of the invention, a method for accuratelymeasuring a magnetic field or a current flowing in a conductor using afiber optics sensor includes the steps of forming an optical path with apolarization maintaining optic fiber, and generating and sending twocounter-propagating linearly polarized light waves traveling in thepolarization maintaining optic fiber on the optical path. The twolinearly polarized light waves are converted into two circularlypolarized light waves traveling on the optical path toward a sensingregion, which pass through the sensing region and experience adifferential phase shift caused by the magnetic field or current flowingin the conductor proximate to the sensing region. The two phase shiftedcircularly polarized light waves are converted back into two linearlypolarized light waves oriented at a relative angle of approximately 45°with respect to one another. The differential phase shift in thecircularly polarized light waves are detected and an output is generatedin response thereto.

A technical advantage of the teachings of the present invention isproviding an extremely economical way to compensate for errorsintroduced in the optical circuit by the quarter waveplates. As aresult, accurate measurement can be achieved without costly orimpractical circuitry or signal analysis and processing.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the present invention, reference may bemade to the accompanying drawings, in which:

FIG. 1 is a schematic diagram of an embodiment of an in-line fiber opticsensor;

FIGS. 2A and 2B are schematic diagrams of the paths taken by the X and Ylight waves along the principle and secondary axes of the fiber toillustrate the problem;

FIG. 3 is a schematic diagram of an exemplary signal processing circuitaccording to the teachings of the present invention;

FIG. 4 is an exemplary plot of the D.C. and harmonic signals of thedetected light output;

FIG. 5 is a block diagram of an exemplary signal processing circuitaccording to the teachings of the present invention; and

FIGS. 6A and 6B are plots of an exemplary modulation signals and thedetected light output according to the teachings of the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

The preferred embodiment of the present invention and its advantages arebest understood by referring to FIGS. 1-6 of the drawings, like numeralsbeing used for like and corresponding parts of the various drawings.

In FIG. 1, a current sensor 10 constructed according to the teachings ofthe present invention comprises a broadband light source 12, whichintroduces a broadband light having multiple optical frequencycomponents into a optic fiber pigtail 14. Optic fiber pigtail 14 ispreferably a length of polarization maintaining fiber. Polarizationmaintaining fiber pigtail 14, is joined to a polarization maintainingbeam splitter or directional coupler 16 where a portion of the light isdirected to a polarizer 18 and the remaining light is terminated at anon-reflective termination point 20. The light beam passes throughpolarizer 18, which linearly polarizes the light. The eigen-axes ofpolarization maintaining fiber pigtail 14, polarization maintaining beamsplitter 16, and polarizer 18 are aligned to one another and to theprinciple axis of light source 12, so as to ensure maximum light inputinto the sensing region. Polarization cross coupling points caused byany misalignment of these axes, in combination with an imperfectpolarizer, may result in the presence of small offsets in the currentmeasurement and should be avoided as much as possible.

After the light passes through polarizer 18, it is divided substantiallyequally into X and Y light waves by a 45° splice 22 into the twoeigen-axes, X and Y respectively, of a birefringence modulator pigtail24. Birefringence modulator pigtail 24 is a section of polarizationmaintaining fiber of sufficient length to depolarize the light passingthrough it. Birefringence modulator pigtail 24 is connected to abirefringence modulator 26, the X and Y eigen axes of these twocomponents being aligned. Birefringence modulator 26 may be anintegrated optics waveguide formed on Ti-indiffused LiNbO₃ with metallicelectrodes surrounding the waveguide. Alternatively, a piezo-electricmodulator may also be used. A voltage applied across the electrodesalters the birefringence of the waveguide. A modulation signal generatedby a waveform generator 28 is applied to the electrodes of birefringencemodulator 26 to dither or phase modulate the light beams. The modulationsignal may be a variety of forms including, for example, sine wavemodulation, square wave modulation, triangle wave modulation, serrodynemodulation, sawtooth modulation, and other suitable periodic waveforms.The modulation signal may also be a combination of a ramp function and aperiodic waveform.

After the light is modulated in birefringence modulator 26, it enters apredetermined length of polarization maintaining fiber bus 30. Theprinciple axes of polarization maintaining fiber bus 30 are aligned tothe principle axes of the birefringence modulator 26. Polarizationmaintaining fiber bus 30 serves two purposes. The first is to carry thelight to a passive sensing medium or sensing fiber 32, which typicallyis remotely located from the active elements such as light source 12 andbirefringence modulator 26. The second purpose of polarizationmaintaining fiber bus 30 is to provide a time delay of sufficient lengththat the modulation signal applied at birefringence modulator 26substantially changes its value during the time it takes for the lightto propagate from birefringence modulator 26 to sensing fiber 32 andreturn. Ideally, the fundamental dither frequency of the waveformapplied to birefringence modulator 26 is 1/2τ or odd multiples thereof,where τ is the propagation time for the light waves to travel frombirefringence modulator 26 through sensing medium 32 and back.

After passing through polarization maintaining fiber bus 30, the lightgoes through a 45° splice 38, a zero or multiple order quarter waveplate 40 set at 45° to the principle axes of the polarizationmaintaining fiber bus 30, and a single mode fiber splice 42. The purposeof quarter wave plate 40 is to convert the orthogonally linearlypolarized light from each of the principle axes of polarizationmaintaining fiber bus 30 to circular states of polarization. The quarterwave plate 40 is preferably constructed from a short section of longbeat length polarization maintaining fiber, ideally a quarter of apolarization beat length long. An odd multiple of quarter beat lengthsof length is also acceptable.

Therefore, two opposingly circularly polarized light waves are generatedby quarter waveplate 40. The X light wave from the first principle axisor X axis of polarization maintaining fiber bus 30 is converted to aright hand circularly polarized (RHCP) light wave. The Y light wave fromthe second principle axis or Y axis of polarization maintaining fiberbus 30 is converted to a left hand circularly polarized (LHCP) lightwave. The two circularly polarized light waves then pass through sensingfiber 32 wrapped around a current-carrying wire 36 at differentvelocities, accumulating a phase difference in proportion to themagnetic field component aligned with sensing fiber 32. Sensing fiber 32may be constructed from a single mode fiber having a low birefringenceper unit length and wound an integral number of turns around currentcarrying wire 36. For most applications, one to five loops of sensingfiber 32 around wire 36 has been shown to be sufficient. It is knownthat birefringence in sensing fiber 32 changes the sensitivity of sensor10 as well as making it sensitive to magnetic fields arising fromexternal sources. The use of a short length of sensing fiber 32 is thusadvantageous for minimizing the total birefringence.

A reflector 44, such as a mirror or mirrored surface, terminates sensingfiber 32. The light is reflected by mirror 44 and passes through sensingfiber 32 again. The sense of circular polarization of the light isreversed upon reflection, causing the right hand circularly polarizedlight wave to be converted to be left hand circularly polarized for itsreturn trip through sensing fiber 32, and vice versa for the left handcircularly polarized light. Since the sense of polarization and thedirection of the light are reversed for both light waves during theirreturn trip through sensing fiber 32, the relative differential phaseshift accumulated between them during the first pass through sensingfiber 32 is doubled during the return trip. The total phase shift, Δφ,accumulated between the two light waves in the double pass sensingregion 60 is thus Δφ=4VNI, where V is the Verdet constant of the fiberglass, N is the number of turns of sensing fiber around current carrywire 36 and I is the current flowing in wire 36.

After the light makes its double pass through sensing fiber 32, thelight wave that was originally in the first principle axis ofpolarization maintaining fiber bus 30 returns to bus 30 linearlypolarized along its second principle axis, and the light wave that wasoriginally in the second principle axis of polarization maintainingfiber bus 30 returns to bus 30 linearly polarized along its firstprinciple axis. The light waves then pass through birefringencemodulator 26 and its pigtail 24 a second time, and are brought togetherand interfered by 45° splice 22 and polarizer 18. A portion of thislight is then coupled to a photodetector 46 via polarization maintainingbeam splitter 16. A signal processing electronics circuit 50 coupled tophotodetector 46 may be used to provide a measurement output.

Therefore, the two light waves underwent exactly the same polarizationevolution throughout the optical circuit, only in reverse order. Becausesensing medium 32 is in-line with respect to the optic fiber, it may beseen that the sensing region around wire 36 is positioned at themidpoint of the optical path traversed by both light waves. Therefore,the only phase difference between the two light waves is that generatedby the presence of a magnetic field in the sensing region.

However, when the quarter waveplate is not perfectly constructed oroperating perfectly, some light traverses the sensing region in thewrong state of circular polarization, thereby causing inaccuratemeasurement. In addition, an extra D.C. light is a byproduct of theimperfect quarter waveplate. The operation of the quarter waveplate isaffected by its operating environment, such as temperature variationsand other external stresses. In particular, the beat length, L_(B),varies with ambient temperature, which is typically 0.1% per ° C.Because the quarter waveplate is typically located remotely from thelight source and other electronics, and is typically exposed to theexternal elements, it encounters large temperature variations. With atemperature differential that can reach, for example, 100° between thehigh temperatures in the Summer and the low temperatures in the Winter,the beat length can change by 10% or more.

Referring to FIGS. 2A and 2B, the paths of the two light waves are shownexplicitly with the approximate relative strengths of the lightcomponents indicated as shown. Imperfect quarter waveplate (IQ) 40converts the X light wave on the first principle axis of the fiber busto right hand circularly polarized (R) light wave and a small left handcircularly polarized (L_(S)) light component due to the imperfection ofquarter waveplate 40. Mirror 44 reflects the light waves and changesthem to left hand circularly polarized light (L) and a small right handcircularly polarized light (R_(S)). The second pass through imperfectquarter waveplate 40 converts the left hand circularly polarized light(L) to a Y light wave on the second principle axis of the fiber bus anda small X light wave (X_(S)) on the first principle axis. The smallright hand circularly polarized light R_(S) is converted to a small Xlight wave (X_(S)) and an even smaller Y light wave (Y_(SS)). The twoX_(S) light components are incoherent with all other light components atthe detector and thus do not provide an interference signal. The twoX_(s) light components comprise one-half of the extra D.C. lightdetected at the photodetector. The Y_(SS) light component results in ascale factor error, where the scale factor is equal to the photodetectoroutput divided by the current in the wire. The affected scale factorcontributes to the computation of inaccurate value for the current. Notethat the subscript S is used to denote the intensities of the lightwaves as compared with the main light wave, which in this case is Y, butis not intended to indicate that the small light wave components havethe same intensity.

As shown in FIG. 2B, the Y light wave traveling on the second principleaxis is similarly converted by imperfect quarter waveplate 40 into twocomponents: left hand circularly polarized light (L) and a small righthand circularly polarized light (R_(S)). Mirror 44 reflects the lightwaves and reverses the sense of polarization of the light waves intoright hand circularly polarized light (R) and a small left handcircularly polarized light (L_(S)). When these two light waves passthrough imperfect quarter waveplate 40 the second time, the right handcircularly polarized light is converted to a main X light wave and asmall Y light wave (Y_(S)), and the small left hand circularly polarizedlight (L_(S)) is converted to a small Y light wave (Y_(S)) and an evensmaller X light wave (X_(SS)). The two Y_(S) light waves traveling onthe second principle axis of the fiber bus comprise the other half ofthe extra incoherent D.C. light detected by the photodetector. TheX_(SS) light component gives rise to an error in the scale factor andresulting in inaccurate current measurement by the sensor.

In both light waves, the resultant extra D.C. light provides a clue tothe magnitude of the X_(SS) and Y_(SS) and thus the scale factor error.Knowing the D.C. and A.C. components and ratio or relative proportion ofthe modulation signals, the relative proportion of the D.C. and A.C.components of the detected light at the detector can be comparedtherewith to determine the magnitude of extra D.C. light or error thatis introduced by the quarter waveplate.

There are two basic methods to compensate for the error caused by theimperfect quarter waveplate and achieve a very accurate currentmeasurement with sensor 10. One method is to vary the wavelength of thebroadband light from light source 12 (FIG. 1) to minimize or eliminatethe extra D.C. light components detected by detector 46. There areseveral ways to vary the wavelength of the light output. For example,the wavelength of light source 12 is affected by changes in ambienttemperature. Therefore, light source 12 may be ed to a heat sink (notshown) and a temperature controller (not shown) that are used to changethe ambient temperature surrounding light source 12. Typically, thewavelength of light source 12 changes by several hundred parts permillion per degree centigrade. However, to compensate for a 100° C.temperature change experienced by the quarter waveplate, for example,the required temperature change for the light source may be greater than100° C. Although achievable, this range of temperature variation may notbe reasonable for most applications.

As another example of a method for varying the source wavelength is toselectively filter very broad spectrum light. The filter is used to varythe range of wavelengths of the resulting broadband light output tocompensate for the errors caused by quarter waveplate thermalvariations. However, this method requires the construction of thewavelength filter, which may be costly.

The method by which the imperfect quarter waveplate is compensated bychanging the wavelength of the incoming light is contemplated herein asdescribed above. However, it may be seen that this method is practicableonly when the temperature variation experienced by the quarter waveplateis relatively small.

The second method for generating accurate sensor operations is tomeasure the extra D.C. light and provide corrections therefor. Theintensity of the light detected by photodetector 46 of FIG. 1 is relatedto the electric current flowing in the wire and to the modulation signalapplied to the birefringence modulator 26 through the relation: ##EQU1##where I_(D) is the total detected power, I_(O) is the power falling onthe photodetector 34 in the absence of electric current andbirefringence modulation, φ(t) is the birefringence modulation waveformpresent in the birefringence modulator, and τ is the round trip delaytime from the birefringence modulator 26 to the end of the sensor 10 andback. In addition to containing a periodic waveform component, φ(t) mayalso contain a ramp-like component, for example, so that the differencebetween φ(t) and φ(t-τ) is a constant plus a periodic waveform.Therefore the modulation signal has a D.C. and an A.C. component. Theslope of the ramp, and thus the value of the constant may be chosen tocancel the electric current induced phase, or 4VNI. Thus, the value ofthe current being sensed may be determined from the slope of the rampnecessary to cause the cancellation to occur.

The above equation may also be written as: ##EQU2## where φ_(m) is ashort hand for the modulation signal which may be a sine wave, forexample.

The apparatus and method for compensating for errors introduced by theimperfect quarter waveplate is to measure the error expressed as asingle number, δ, and correct the scale factor to arrive at the accuratemeasurement. δ is derived by defining a Jones matrix, L which describesthe element that is intended to convert linearly polarized light tocircularly polarized light. In the embodiment of the present invention,a quarter waveplate set at 45° to the birefringent axes of thepolarization maintaining fiber bus is used for the conversion. Ingeneral, L can be expressed as: ##EQU3## where p, q, r, s are realnumbers and j=√-1. This way of expressing L is a general result foroptical elements having polarization independent loss. For an idealquarter waveplate set at 45°, we obtain p=1/2, q=-1/2, r=1/2, ands=-1/2. Then, δ is defined as 2(ps+qr)+1, where ideally, δ=0 when thequarter waveplate is operating perfectly and not influenced by externalstresses.

Analyzing the fiber optics sensor using the Jones Matrix, including L asa general element, the detected light can be expressed as: ##EQU4##Dropping δ², making γ=0, and using K to represent a constant dependenton the intensity of the detected light, the detected light becomes:

    I.sub.D =K{1-δ cos (φ.sub.m cos ωt)+(1-δ) cos (4VNI+φ.sub.m cos ωt)}                          (6)

which is the equation used to analyze the solutions to the inaccuratecurrent measurement problem.

If the quarter waveplate error or δ is zero, then there is a fixedrelationship between the D.C. component of the detected light and allthe harmonic signals therein. When δ is not zero, the proportion betweenthe D.C. and the harmonic signals are corrupted.

Referring to an exemplary circuit 60 shown in FIG. 3, a peak detector 62and a lock-in demodulator 64 are both coupled to photodetector 46 toreceive an input representative of the light detected thereby. Theoutput from photodetector 46 may be voltage level or current. Peakdetector 62 determines the maximum level of the photodetector output,and lock-in demodulator demodulates the signal and provides theamplitude of the signal. The output of lock-in demodulator 64 and theoutput of peak detector 62 are coupled to a divider 66.

In operation, peak detector 62 provides the maximum level of thephotodetector output, which may be expressed as:

    I.sub.DMAX =2K(1-δ)                                  (7)

The output of lock-in demodulator essentially provides the firstharmonic signal of the output, which may be expressed as:

    I.sub.1H =2KJ.sub.1 (φ.sub.m)4VNI(1-δ)           (8)

where J₁ is the Bessel function. The output from lock-in demodulator 64divided by the output from peak detector 62 yields: ##EQU5## Thisequation is independent of δ and thus can be used to solve for thecurrent, I, since all other parameters are known. It may be deduced fromthe foregoing that a microprocessor-based signal analysis system mayalso be used to accomplish the same or similar functions as the peakdetector and lock-in modulator to derive the ratio and compare it withthe expected ratio based on the modulation waveform inputs.

Referring to FIG. 4, a diagram of the D.C. component as well as someharmonic signals of the detected light is shown. It may be seen that theharmonic signals of the detected signal is on the order of (1-δ).Therefore, any one of the harmonic signals can be divided by any signalfrom the detected light that is also proportional to (1-δ). In theimplementation described above, the numerator is the first harmonicsignal and the denominator is the peak value of the detected light.However, it may be seen that any signal component that can be isolatedout of the detected light can be used in a similar manner to derive theratios.

Further, it may be seen from the foregoing that the teachings of thepresent invention provides for a comparison of the D.C. component of thedetected light to the A.C. spectrum when no quarter waveplate errors arepresent, which is then used as the basis for comparison when errors arepresent. The apparatus and method described above provides for acomparison between the peak level, which is a combination of the D.C.signal and all the harmonics, and the first harmonic signal. However,the invention also contemplates other means of comparison to derive therelationship between the D.C. signals and the harmonic signals. Forexample, the second harmonic signal may be measured and divided by themeasured D.C. signal to establish the basis for comparison forsubsequent measurements that may include quarter waveplate error.

Referring again to the equation:

    I.sub.D =K{1+cos [4VNI+φ(t)-φ(t-τ)]}           (10)

Using a ramp function in addition to a periodic waveform at thebirefringence modulator, the detected light becomes:

    I.sub.D =K[1+cos (4VNI+γ+φ.sub.m cos ωt)]  (11)

where γ is a constant proportional to the slope of the ramp function. Ifγ=-4VNI, then the detected light is:

    I.sub.D =K[1+cos (φ.sub.m cos ωt)]               (12)

Therefore, by setting γ=-4VNI, the first harmonic signal of this outputbecomes zero. By changing the value of γ that is introduced into thesystem to zero out the first harmonic signal, the desired output isderived from the slope of the ramp function or saw tooth waveform.

Referring to FIG. 5 for a block diagram of an exemplary circuitimplementation of the signal processing electronics, the slope of theramp function or saw tooth waveform may be determined by using a counter72 to count the number of saw tooths occurring during a specified timeperiod. The higher the count corresponds to more steepness in the rampslope. The counter output is thus proportional to γ.

Due to errors introduced by the quarter waveplate, γ≠-4VNI but willactually be proportional to (1+δ):

    γ=-4VNI(1+δ)                                   (13)

To cancel out δ, we may divide γ with a term that is proportional to(1+δ). Alternatively, γ may be multiplied with a term that isproportional to (1-δ) to generate a value proportional to (1-δ²), whichis approximately 1 for small δ.

Using sine wave modulation on the birefringence modulator in addition tothe saw tooth waveform so that:

    φ(t)-φ(t-τ)=γ+φ.sub.m cos ωt   (14)

and choosing φ_(m) =π/2: ##EQU6## Alternatively, with φ_(m) =2.4:##EQU7## Thus, either of these methods may be used to obtain a suitablenormalizing factor that removes the δ dependence inherent in γ.

Referring to FIG. 6A, if square wave modulation is used on thebirefringence modulator in addition to the ramp function or saw toothwaveform, then [φ(t)-φ(t-τ)] is equal to γ plus a more complicatedperiodic waveform. Choosing τ≠1/2 duty cycle for off-proper frequencyoperation, the resultant photodetector output is:

    I.sub.D =K[1+cos φ.sub.m (t)]                          (17)

which is shown in FIG. 6B. Therefore, with a nonzero δ, and φ_(m) =π/2:##EQU8## which may be used as the normalizing factor to remove thedependence on δ that is inherent in γ.

Yet another solution to the scale factor error caused by imperfectquarter waveplates in a loop configuration of the optical sensor is thesubject matter of another invention. The loop fiber optic sensor isdescribed in detail in Blake. In the loop configuration, two quarterwaveplates are disposed in the optical path at either side of thesensing medium. In the teachings of this invention, the solutionprovides for the orientation of quarter waveplates of approximately 45°with one another. It is shown below that the orientation of the quarterwaveplates is 45° plus a rotation angle caused by the circularbirefringence in the sensing medium. The quarter waveplates convert thepolarization state of the counter-propagating light waves from linear tocircular before entering the sensing region and back to linear afterexiting the sensing region. The two counter-propagating light wavesfollow the same path and as a result there is a non-reciprocal phaseshift only in the presence of a magnetic field in the current carryingwire. In this case, the effective refractive index seen by thecircularly polarized light beams going in the opposite directions alongthe sensing loop is different. Thus, a non-reciprocal phase shiftbetween the two light beams is induced, which is proportional to themagnetic field, Δφ=2VNI, where I is the electric current in the wire, Vis the Verdet constant of the fiber glass and N is the number of turnsin the sensing loop. For simplicity, we substitute F for VNI in theequations set forth below.

Under ideal conditions, when the delay introduced by the quarterwaveplates is 90°, the linearly polarized light wave is perfectlyconverted to one circular state before its trip through the sensingfiber. An imperfect quarter waveplate, on the other hand, converts thelinearly polarized light into a mixture of both right and left handcircularly polarized light waves. The unwanted circularly polarized beamaccumulates the wrong phase shift, but if the second quarter waveplateis ideal, the light wave in the wrong state of circular polarization isconverted to the orthogonal axis with respect to the main polarizationand is eventually rejected by the polarizer. So, even if one of thequarter waveplates is imperfect, there is no scale factor error.However, if both quarter waveplates are imperfect, a small portion oflight with the wrong phase is converted into the pass axis of thepolarizer and falls on the detector, thereby introducing a scale factorerror. The magnitude and the sign of this error depends on the qualityof the quarter waveplates and the relative angle between their axes.

The current sensor may be modeled by the Jones matrix to analyze thepolarization evolution of the light within the fiber and calculate thephase difference between the two counter-propagating beams. For the wavepropagating in the clockwise direction (CW), we have the following:##EQU9## δ₁ and δ₂ are the phase delays between the two polarizationsintroduced by the quarter waveplates and F is the polarization rotationinduced due to the Faraday effect. The angle θ, in general, includes therelative angle between the axes of the quarter waveplates, and thepolarization rotation due to circular birefringence in the sensingfiber. In the absence of circular polarization, θ=0° corresponds toaligning the quarter waveplate axes fast to fast. For thesecalculations, an assumption is made that the axes of the quarterwaveplates are aligned 45° with respect to the polarizer, which is aperfect device. Both these conditions can easily be achieved to a highaccuracy in real systems.

To describe the propagation of the oppositely traveling light wave, thecomposite Jones matrix is transposed, and the sign of the off-diagonalelements is reversed, and the sign of the Faraday angle F is alsoreversed. This convention preserves a right handed coordinate systemwith light propagation always to be in the +z direction. Aftermultiplying out the matrices and calculating the phases of the complexamplitudes representing the electric fields of the twocounter-propagating waves: ##EQU10##

For ψ=θ-90°, where in the absence of circular birefringence ψ is thephysical angle between the eigen axes of the polarization maintainingfibers adjoining the two quarter waveplates. The phase difference is:##EQU11##

For imperfect quarter waveplates we express the sum and the differenceof the retardation angles in terms of the sum and difference of theerrors δ₁ =δ₂ =180°+ε.sub.Σ and δ₁ -δ₂ =ε.sub.Δ, where ε.sub.Σ is thesum of the quarter-wave errors and ε.sub.Δ is the difference betweenthem. Defining ##EQU12##

If the fast axis of one quarter waveplate is aligned to the slow axis ofthe other, the physical angle between the polarizers ψ is 0°, then fromEquation (35) for small deviations of the retardation angle from 90° andsmall Faraday rotations, the phase difference is proportional to theproduct of the quarter waveplate errors. ##EQU13## where ε=δ₁ -90° andε₂ =δ₂ -90°. If we align the fast axis of one quarter waveplate to thefast axis of the other, the angle between the polarizers, ψ, is equal to90°, and the scale factor dependence remains quadratic with respect tothe quarter waveplate error, but the sign in front of the quadraticequation term changes: ##EQU14##

The question now is whether it is possible to find an angle between thepolarizers such that the dependence of the scale factor on the qualityof the quarter waveplates in the vicinity of ε₁ and ε₂ ≅0, (smallerrors), is minimized. In Equation (35) g is substituted with 1-h, whereh is a small value, and after ignoring any h² terms and applying thetrigonometric identities the phase difference is found to be: ##EQU15##

It is desirable that this phase difference is independent of h.Therefore, the condition on the optimum angle ψ between the polarizersis: ##EQU16## or ψ=45°. Unlike the quadratic dependence of the scalefactor on the error of the quarter waveplate for 0° and 90° alignmentsshown by Equations (36) and (37), for a 45° alignment, the scale factorchanges as (ε²)², which makes the scale factor less sensitive to changesin the retardation angle of the quarter waveplate. ##EQU17##

In the presence of a magnetic field in the sensing loop, the parasiticlight wave accumulates a phase shift with respect to the main beam. Thisphase shift depends on the relative alignment of the quarter waveplateaxes and results in changes in the scale factor when the light with thewrong sense of circular polarization is mixed with the main lightthrough the imperfect quarter waveplate. At 45° between the quarterwaveplate axes (fast-to-fast, slow-to-slow, and fast-to-slow axes), theeffect of this parasitic wave is minimized. For example, to maintain ascale factor accuracy of approximately 0.3% without using this alignmentconfiguration requires a quarter waveplate with a retardation of90±4.4°; with it, the sensor can tolerate a quarter waveplate with aretardation of approximately 90±22.30°. To provide 100 ppm stability,this alignment configuration can tolerate a quarter waveplate ofapproximately 90±9.6°, whereas without it, a quarter waveplate mustpossess a retardation of about 90±0.8°.

Thus, when the angle between the polarizers is 45°, even largedeviations from the ideal 90° retardation of the quarter waveplates canbe tolerated, thus eliminating the dependence of the scale factorstability on the quality of the quarter waveplates.

When the optical sensor includes a sensing medium that introducescircular birefringence, the rotation caused thereby should be taken intoaccount in the quarter waveplate orientation. For example, if thepolarization of the light waves rotates by 45° due to circularbirefringence in the sensing medium, then the quarter waveplates shouldbe oriented (45°+45°) or 90° with respect to each other. Therefore, thequarter waveplate orientation is 45° plus the degree of rotation inducedby circular birefringence in the fiber in order to eliminate or minimizethe scale factor error.

Although the present invention and its advantages have been described indetail, it should be understood that various mutations, changes,substitutions and alterations can be made therein without departing fromthe spirit and scope of the invention as defined by the appended claims.

What is claimed is:
 1. A fiber optics sensor, comprising:a polarizationmaintaining optic fiber forming an optical path; first and secondcounter-propagating linearly polarized light waves traveling in thepolarization maintaining optic fiber on the optical path; a firstquarter waveplate coupled to the optic fiber and disposed in the opticalpath generally adjacent to a sensing region, the first quarter waveplateoperable to convert the first linearly polarized light wave into acircularly polarized light wave traveling on the optical path prior tothe sensing region; a second quarter waveplate coupled to the opticfiber and disposed in the optical path adjacent to the sensing region,the second quarter waveplate operable to convert the second linearlypolarized light wave into a second circularly polarized light wave priorto the sensing region; the first and second quarter waveplates beingoriented with one another at approximately 45°; the second quarterwaveplate further operable to convert the first circularly polarizedlight wave back to a first linearly polarized light wave after exitingthe sensing region; the first quarter waveplate further operable toconvert the second circularly polarized light wave back to a secondlinearly polarized light wave after exiting the sensing region; thesensing region including a sensing medium coupled to the polarizationmaintaining optic fiber and being substantially equidistant from thefirst and second quarter waveplates, the first and second circularlypolarized light waves passing through the sensing medium experiencing adifferential phase shift caused by a magnetic field or current flowingin a conductor proximate to the sensing region; a detector coupled tothe optic fiber detecting the differential phase shift and producing anoutput in response thereto.
 2. The fiber optics sensor, as set forth inclaim 1, wherein the first and second quarter waveplates are oriented,with respect to one another, at 45° plus an amount of rotation inducedby a circular birefringence in the sensing medium.
 3. The fiber opticssensor, as set forth in claim 1, further comprising a phase modulatorcoupled to the polarization maintaining optic fiber for applying atleast one modulation waveform to phase modulate the two linearlypolarized light waves.
 4. The fiber optics sensor, as set forth in claim1, wherein the sensing medium is an optical fiber.
 5. The fiber opticssensor, as set forth in claim 1, wherein the sensing medium is a lowbirefringence optical fiber.
 6. The fiber optics sensor, as set forth inclaim 1, wherein the polarization maintaining optic fiber forms a loop,the sensing medium being located substantially mid-point of the opticfiber loop.
 7. A fiber optics sensor, comprising:a polarizationmaintaining optic fiber forming an optical loop; a sensing mediumcoupled to the optic fiber and disposed generally midway in the opticalloop; first and second quarter waveplates, coupled to the optic fiberand oriented at approximately 45° with one another in close proximity tothe sensing medium, being operable to convert two counter-propagatinglinearly polarized light waves into two counter-propagating circularlypolarized light waves prior to passing through the sensing medium, andconverting the counter-propagating circularly polarized light waves intotwo linearly polarized light waves after exiting the sensing medium, thecounter-propagating circularly polarized light waves passing through thesensing medium experiencing a differential phase shift caused by amagnetic field or current flowing in a conductor proximate to thesensing medium; and a detector coupled to the optic fiber detecting thedifferential phase shift and producing an output in response thereto. 8.The fiber optics sensor, as set forth in claim 7, wherein the first andsecond quarter waveplates are oriented, with respect to one another, at45° plus an amount of rotation induced by a circular birefringence inthe sensing medium.
 9. A method for accurately measuring a magneticfield using an optical sensor, comprising the steps of:forming apolarization maintaining optical path; generating and sending twocounter-propagating linearly polarized light waves traveling on theoptical path; converting the two linearly polarized light waves into twocircularly polarized light waves traveling on the optical path toward asensing region; passing the circularly polarized light waves through thesensing region which experience a differential phase shift caused by themagnetic field; converting the two phase shifted circularly polarizedlight waves back into two linearly polarized light waves oriented at arelative angle of approximately 45° with respect to one another; anddetecting the differential phase shift in the circularly polarized lightwaves and producing an output in response thereto.
 10. The method, asset forth in claim 9, wherein the two phase shifted circularly polarizedlight converting step further comprises the step of converting the phaseshifted circularly polarized light waves back into two linearlypolarized light waves oriented at a relative angle of approximately 45°plus a rotation angle with respect to one another, the rotation anglebeing caused by a circular birefringence in the sensing region.
 11. Anoptical interferometric sensor for detecting a magnetic field,comprising:an optical path having an initiating end and a terminatingend; means disposed in the optical path for generating co-located righthand circularly polarized light wave and left hand circularly polarizedlight wave traveling along the optical path in a first direction fromthe initiating end toward the terminating end of the optical path; asensing medium sensitive to the magnetic field disposed in the opticalpath proximate to the terminating end of the optical path, theco-located circularly polarized light waves passing through the sensingmedium in a first direction, the magnetic field inducing a differentialphase shift in the light waves; a reflector coupled to the sensingmedium and terminating end of the optical path and reflecting andreversing the polarization sense of the right and left hand circularlypolarized light waves, the reflected circularly polarized light wavesreturning through said sensing medium in a second direction toward saidinitiating end of the optical path; and a detector coupled to saidinitiating end of said optical path operable to detect said differentialphase shift in said light waves and producing an output in responsethereto.
 12. An optical interferometric magnetic field sensor,comprising:a polarization maintaining optical path; two linearlypolarized light waves traveling in said polarization maintaining opticalpath; at least one quarter waveplate disposed at substantially amid-point in said optical path for converting the two linearly polarizedlight waves into two opposingly circularly polarized light wavestraveling on the optical path toward a sensing region; said sensingregion including a sensing medium sensitive to a magnetic field disposedat generally the mid-point in the optical path, the opposing circularlypolarized light waves passing through the sensing medium, and themagnetic field causing a differential phase shift in the opposinglycircularly polarized light waves; and a detector operable to detect thedifferential phase shift and producing an output in response thereto.13. The optical interferometric sensor, as set forth in claim 12,comprising first and second quarter waveplates, the first and secondquarter waveplates are oriented, with respect to one another, at 45°plus an amount of rotation induced by a circular birefringence in thesensing medium.
 14. The optical interferometric magnetic field sensor,as set forth in claim 12, wherein the polarization maintaining opticalpath is formed by a polarization maintaining optical fiber.
 15. Anoptical interferometric sensor, comprising:a polarization maintainingoptical loop; a sensing medium sensitive to a magnetic field disposed inthe optical loop; first and second quarter waveplates disposed in theoptical loop and oriented with respect to one another at approximately45° plus an amount of rotation induced by a circular birefringence inthe sensing medium for converting two counter-propagating linearlypolarized light waves into two counter-propagating circularly polarizedlight waves prior to passing through the sensing medium, and convertingthe circularly polarized light waves into linearly polarized light wavesafter exiting the sensing medium, the magnetic field inducing adifferential phase shift in the circularly polarized light waves passingthrough the sensing medium; and a detector coupled operable to detectthe differential phase shift and producing an output in responsethereto.